case study of accounting
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LectureNote6-CapitalBudgeting.pptxLecture 6: Capital Budgeting Berk, DeMarzo 3rd edition, Chapter 8 Section 8.1-8.4
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Outline
Capital Budgeting
To evaluate projects, use Discounted Cash Flow (DCF) Analysis
Considerations in DCF Analysis
Opportunity Costs, Sunk Costs, Cannibalization …
Examples
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Which projects to take?
The table shows the projects that Elon Musk’s (the CEO of Tesla and SpaceX) companies are taking on. Put yourself in his shoes and think about how you should determine which projects to take on.
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Capital Budgeting
Capital Budget
Lists the projects and investments that a company plans to undertake
Capital Budgeting
Process used to analyze alternative investments and decide which ones to accept
Goal: decide to accept or reject a project based on its cash flow and NPV.
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Capital Budgeting
Steps:
Estimate incremental cash flows in the project
The amount by which a firm’s cash flows are expected to change as a result of the investment decision.
Determine a cost of capital used for discounting
Calculate NPV
Accept or reject the project
This process is also called as Discounted Cash Flow analysis (DCF)
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See notes underneath the slide
1.
Example of “Incremental”:
Suppose your firm is considering replacing outdated equipment with a new piece of equipment which is more efficient. The sales in the past year is $10,000, and you expect the new equipment will generate sales of $15,000 each year, then the incremental sales in each year is $5,000.
Note $5,000 is the incremental sales, not incremental cash flows, because there might be other costs, such as depreciation, and tax benefit of depreciation deduction.
Of course, you also have a cash outflow (purchasing equipment) at the beginning.
2.
For now, we assume that the cost of capital is given, and we focus on the rest steps, especially the first step (most challenging part), estimating the incremental cash flows.
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Example
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See notes underneath the slide
Example:
Suppose you have an investment opportunity (e.g. purchase equipment), where you need to spend $90,000 (e.g. on equipment) at Year 0 (NOW). The salvage value (see below for definition) at the end of the asset is $0. For simplicity, we assume the project life is the same as the life of asset (3 years). Based on the forecast of sales and costs, change in net working capital, tax rate, and opportunity cost of capital (for discounting), should we accept this project?
I want you to think about two things when evaluating a project.
The components of cash flows (i.e., what contribute(s) to the cash flows?)
2. How does each factor affect the cash flow and your valuation?
For example
The more sales you have, all else equal, you should have more cash flows.
The higher tax rate, the less cash flows you will receive.
How does change in net working capital affect cash flows.
Definition:
Salvage value is the estimated value of property at the end of its useful life. It is what you expect to get for the property if you sell it after you can no longer use it productively.
The opportunity cost of capital (see lecture 3) is the best available expected return offered in the market on an investment of comparable risk and term. It provides the benchmark against which the cash flows of a new investment should be evaluated.
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Typical Project Cash Flows
cash flow from change in net working capital
cash flows from net income with depreciation added back
Cash flow from investment
See notes underneath the slide
For each stage, I want you to think about how each term will affect cash flows.
Start-up stage
purchasing equipment will reduce the cash available to a firm (this is cash flow from investment)
increases in net working capital (e.g. increase in inventory, account receivable, or decrease in account payable) will reduce the cash available to a firm (cash flow from change in net working capital, ∆NWC)
e.g. you buy beans before you open a coffee shop, inventory increases, net working capital increases, and this increase in NWC reduces the cash available to a firm.
note that decrease in accounts payable (everything else equal) will increase the net working capital (NWC) because NWC= inventory + accounts receivable – accounts payable
On-going
You have sales, costs, and net income, which will affect cash flows (cash flows from net income and depreciation)
recall we need to convert net income to operating cash flows
Change in NWC (again not the level) also affects the cash flows (cash flow from change in net working capital, ∆NWC)
Shut-down
Note the decrease in NWC will release the cash tied to NWC and increase the cash available to a firm (cash flow from change in net working capital, ∆NWC)
e.g. when you close a coffee shop, you want to sell you beans (i.e. decrease in NWC), which increases the cash available to you.
And you also want to collect any account receivable (i.e. decrease in NWC), which also increases the cash available to you.
Ultimately, the cash flows are affected by the following three parts:
cash flows from net income and depreciation
cash flows from change in net working capital, ∆NWC
cash flows from investment
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Follow the Cash!!
Discount cash flows, not profits!!!!!!!
Most analysis will start with an accounting projection (forecast sales, costs, depreciation, and net income)
Net income must be converted to cash flows for NPV analysis
Recognize all cash flow effects
Cash flows from net income with depreciation added back
Cash flows from change in net working capital (∆NWC)
Cash flows from investment
Convert net income to operating cash flows
See notes underneath the slide
Check the notes underneath the figure on typical project cash flows (previous slide) to see all cash flow effects I, II, and III.
We include the cash flows from I and II when we convert net income to operating cash flows in the last lecture. The incremental effect of a project on a firm’s available cash also includes the cash flows from investment.
Operating cash flow is a measure of the amount of cash generated by a company's normal business operations.
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∆Net Working Capital and Operating Cash Flows
Simplify:
Net Income
+ depreciation
- change in accounts receivable (change: current – previous)
- change in Inventory
+ change in accounts payable
Operating cash flow (Cash Flow from Operations)
Get:
Net Income
+ depreciation
- change in Net Working Capital (NWC= AR + Inventory - AP)
Operating cash flow
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last lecture
See notes underneath the slide
Simplification steps:
- change in accounts receivable
- change in Inventory
+ change in accounts payable
=
- change in (accounts receivable + Inventory - accounts payable)
=
- change in Net Working Capital (NWC= AR + Inventory - AP)
Note:
change in NWC matters, NOT the level of NWC
The cash effect of ∆NWC is NEGATIVE ∆NWC.
any increases in net working capital represent an investment that reduces the cash that is available to the firm.
e.g. when ∆NWC = $100, the cash effect of ∆NWC is NEGATIVE $100. To help understand or remember this, you can think that $100 of ∆NWC is just an increase in inventory (e.g., buy extra beans for your coffee shop, holding all other components of NWC constant), which reduces the cash available to you, so the cash effect is NEGATIVE $100
e.g. when ∆NWC = NEGATIVE $100, the cash effect of ∆NWC is POSITIVE $100. To help understand or remember this, you can think that negative $100 of ∆NWC is just an decrease in inventory or accounts receivable, which increases the cash available to you, so the cash effect is POSITIVE $100
FYI.
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(p242 of Berk DeMarzo 3rd edition)
The text also includes cash in NWC calculation.
But be cautious that the cash is the cash tied to operation (e.g. cash held in cash registers for retail stores, similar to cash tied to inventory), such tied cash should be included in NWC calculation.
Note that for valuation purpose, NWC should EXCLUDE the cash that is invested to earn a market rate of return, because ultimately we will discount the incremental cash flows generated the project by an opportunity cost of capital that reflects the risk of the project, but cash, especially in large amounts, is invested by firms in treasury bills, short term government securities or commercial paper (e.g., at the end of 2008Q3, Apple has $243.7 billion cash, such cash (at least most cash) is unlikely to be tied to operations, but is rather invested to earn a market rate of return). They represent a fair return for riskless investments, so we should exclude such cash in NWC calculation.
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Discounted Cash Flow Issues for NPV Analysis
Only incremental cash flow matters.
Separate Investment and Financing Decisions.
When evaluating a capital budgeting decision, we generally do not include interest expenses.
Evaluate a project as if it will not use any debt to finance it (so unlevered). The corresponding net income is called unlevered net income.
Unlevered net income = EBIT * (1 – tax rate)
= (Revenues - Costs - Depreciation) * (1 – tax rate)
NO interest expense here
See notes underneath the slide
We generally exclude interest expense because any incremental interest expenses will be related to the firm’s decision regarding how to finance the project. Here we wish to evaluate the project on its own, separate from the financing decision.
As a result, in unlevered net income calculation, there is NO interest expense.
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Free cash flow
Free cash flow (FCF): the incremental effect of a project on the firm’s available cash
FCF is the cash flow “free” to be distributed to investors
Unlevered net income
+ depreciation
- change in Net Working Capital
= Operating cash flow
- Cash flow from investment (Capital expenditure or CapEx)
= Free cash flow
Discount FCFs to get the NPV of a project.
Convert net income to operating cash flows
See notes underneath the slide
We have seen how to convert net income to operating cash flows. We just need to take out the cash flow from investment to get FCF.
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Free cash flow
Discount FCFs back to Year 0 (today) to get the NPV of a project.
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| Year | 0 | 1 | 2 | 3 |
| Unlevered Net Income | ||||
| Add Back Depreciation | ||||
| Subtract Change in NWC | ||||
| Subtract Capital Expenditure | ||||
| Free Cash Flow |
See notes underneath the slide
convention:
In capital budgeting, a project starts at year 0, which is today.
If the project is to purchase a new piece of equipment, then the cash flow occurs at date 0, and the depreciation starts from Year 1 to the end of its useful life (to match the sales)
The sales generated by the equipment will start from Year 1, NOT Year 0.
The firm needs to put in net working capital (e.g. buy beans for coffee shop) at Year 0 before it can sell its products in Year 1, so the level of net working capital at Year 0 is positive, so is the change in NWC at Year 0.
See the solution to the in-class exercise (in the last slide) on blackboard.
Pay special attention to the signs of change in NWC.
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Calculating unlevered net income
Recall the first step in evaluating a project is to forecast the incremental revenue and cost generated by the project.
In this step, we can get unlevered net income = (Revenues - Costs - Depreciation) * (1 – tax rate)
Again, it is important to identify revenues and costs that are generated only because of the project.
So only incremental revenues and incremental costs.
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Pro-Forma Financial Statements
Pro-Forma Statement: financials under a set of hypothetical assumptions
Sales
- Cost of Goods Sold
Gross Profit
- Selling, General, and Administrative expenses
EBITDA
- Depreciation
EBIT
- Tax
Unlevered Net income (excluding Interest)
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See notes underneath the slide
This is what a pro-forma net income statement looks like.
We make assumptions on the sales, costs, depreciation and etc, and based on these assumptions, we can calculate unlevered net income.
Note all revenues and costs are incremental.
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Other Issues
Interest Expense
Not included in capital budgeting because we separate investment and financing decisions.
Which tax rate to use?
Corporate Taxes - Paid by the corporation out of profits before shareholders are paid.
System is progressive - Tax rate generally increases with income.
Marginal Tax Rate - Tax Rate on next dollar of income.
Average Tax Rate - Taxes paid/Pretax income
In capital budgeting, use Marginal Tax Rate because it captures the incremental effect of the project.
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See notes underneath the slide
A firm generally identifies its marginal tax rate by determining the tax bracket that it falls into based on its overall level of pretax income.
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Marginal vs. Average Corporate Tax Rates
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Note that while marginal rates fluctuate and rise as high as 39%, average rates increase steadily with taxable income, until the 35% level is reached.
See notes underneath the slide
For example, if a firm’s current taxable income falls into the bracket of $0-50,000, say $50,000, and it expect the new project will generate a pre-tax income of 20,000, then for the new project, you should use the marginal tax rate of 25%.
But if the firm’s current taxable income falls into the bracket of $50,001-75,000, say $75,000, and it expect the new project will generate the same pre-tax income of 20,000, then for the new project, you should use the marginal tax rate of 34%.
Bottom line: use marginal tax rate for capital budgeting.
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Net Effect of Depreciation
Unlevered net income
+ depreciation
- change in Net Working Capital
= Operating cash flow
- Cash flow from investment (Capital expenditure or CapEx)
= Free cash flow
Question:
Where does deprecation show up in FCF estimation?
What is the net effect of depreciation on FCF?
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See notes underneath the slide
Depreciation shows up in two places.
when calculating unlevered net income, we deduct depreciation from sales.
when we add back depreciation to net income.
However, the net effect of depreciation is NOT zero, because of tax (see next slide).
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Depreciation tax shield
Note: first deduct depreciation when calculating unlevered net income, then add back depreciation to the taxable net income.
Simplify FCF:
The net effect of depreciation on FCF is:
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Called depreciation tax shield.
Positive effect on FCF
See notes underneath the slide
The larger depreciation, the higher FCF.
Why do we care about the net effect of depreciation on FCF, because financial managers care, why? You will see why it matters in few slides.
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Depreciation Methods
Straight-line depreciation
Annual depreciation =
depreciation = ___ in slide 6?
Accelerated depreciation method (e.g. MACRS, modified accelerated cost recovery system)
Depreciate more in earlier years
How does that affect free cash flows and NPV?
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See notes underneath the slide
In the example in slide 6, the annual depreciation is Purchase value 90,000 minus salvage value 0, then divide by a 3-year life, so annual depreciation is $30,000.
Accelerated depreciation
In practice the tax code allows a firm to “accelerate” the depreciation on the theory that an asset loses more value in the early years.
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This table shows the schedule of MACRS (an accelerated depreciation)
FYI: MACRS only allows a half year of depreciation the year an asset is put in service (half-year convention)
Bottom line: in an accelerated depreciation schedule, assets depreciate more rapidly in early years.
See notes underneath the slide
FYI:
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In the table of MACRS depreciation, you can find that for 3-year recovery, the depreciation is allowed in the first 4 years, not 3 years, because of the “half-year convention”.
Half-year convention. The half-year convention is used to calculate depreciation for tax purposes, and states that a fixed asset is assumed to have been in service for one-half of its first year, irrespective of the actual purchase date.
The lower amount in year 1 reflects a “half-year convention” in which the asset is presumed to be in use (and this depreciated) for half of the first year, no matter when it was
actually put into use. After year 1, it is assumed that the asset depreciates more rapidly in earlier years.
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Accelerated Depreciation Example
Which depreciation schedule has more tax savings?
Assume tax rate =30%, discount rate = 15%.
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| Year | Accelerated Depreciation 3 Year | Annual Depr. | Tax Savings | Straight Line 3 Year | Tax Savings |
| 1 | 50% | $30,000 | $9,000 | $20,000 | $6,000 |
| 2 | 30% | $18,000 | $5,400 | $20,000 | $6,000 |
| 3 | 20% | $12,000 | $3,600 | $20,000 | $6,000 |
| PV of Tax Savings @ 15 % | ? | PV of Tax Savings @ 15 % | ? |
See notes underneath the slide
Question:
Suppose the new equipment costs $60,000. There are two depreciation schedules, straight-line depreciation and accelerated depreciation schedules, which one has more tax savings? Assume tax rate is 30% and discount rate is 15%.
Note this accelerated depreciation schedule is hypothetical, just showing that the asset depreciates more rapidly in early years. It is NOT the schedule in MACRS (MACRS is allowed by IRS).
Answer:
First, note that the net effect of depreciation on FCF is tax rate*depreciation (depreciation tax shield), so POSTIVE effect on cash flows.
For both schedules, we will have tax savings for three years. To compare the tax savings, we discount tax savings to Year 0 (today).
Calculation:
For accelerated depreciation.
1.1 Calculate annual depreciation for each year,
60,000 * 50% =$30,000 for Year 1
60,000 * 30% =$18,000 for Year 2
60,000 * 20% =$12,000 for Year 3
1.2 Calculate the tax savings, tax rate (30%)*depreciation
e.g. for year 1, tax savings = $30,000 * 30% = 9000
1.3 Discount the 3-year tax savings to present, so
PV = 9000/1.15 + 5400/1.15^2 +3600/1.15^3 = $14,276
2. Similarly, you can get the PV of tax savings for straight-line depreciation, which is $13,699.
Bottom line: the accelerated depreciation has more tax savings. Because depreciation contributes positively to the firm’s cash flow through the depreciation tax shield, it is in the firm’s best interest to use the accelerated depreciation.
Intuition: in an extreme case, in the next three years, would you prefer to receive the cash flows 6, 0, 0 or 0, 0, 6?
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Terminal Value
Idea: Sometimes firms explicitly forecast free cash flow over a shorter horizon than the full horizon of a project, then calculate an additional, one-time cash flow at the end of the forecast horizon.
This one-time cash flow is called terminal value. It represents the market value of the free cash flow from the project at all future dates.
PV(all cash flows) = PV(cash flows in the short horizon) + PV(Terminal value)
Caution: remember to discount terminal value.
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See notes underneath the slide
Sometimes the firm explicitly forecasts free cash flow over a shorter horizon than the full horizon of the project or investment. This is necessarily true for investments with an indefinite life, such as an expansion of the firm.
In this case, we estimate the value of the remaining free cash flow beyond the forecast horizon by including an additional, one-time cash flow at the end of the forecast horizon called the terminal or continuation value of the project.
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Terminal Value Example
Problem (from textbook page 251)
Base Hardware is considering opening a set of new retail stores. The free cash flow projections for the new stores are shown below (in millions of dollars):
After year 4, Base Hardware expects free cash flow from the stores to increase at a rate of 5% per year. If the appropriate cost of capital for this investment is 10%, what terminal value in year 4 captures the value of future free cash flows in year 5 and beyond? What is the NPV of the new stores?
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See notes underneath the slide
Do you recognize that part of the cash flow streams look like a growing perpetuity?
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Solution
Because the future free cash flow beyond year 4 is expected to grow at 5% per year, the terminal value in year 4 of the free cash flows in year 5 and beyond can be calculated as a constant growth perpetuity:
(why? b/c Year N Terminal Value = Year N+1 FCF/(r-g))
Note this terminal value is at Year 4.
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See notes underneath the slide
1.
The free cash flows from year 5 and beyond are 1.3*1.05, 1.3*1.05^2, 1.3*1.05^3, …
Review the slides 32-34 of lecture note 2, if you forgot how to calculate growing perpetuity.
Note that to use the growing perpetuity formula C/(r-g), where the first payment is C. Here in this growing perpetuity 1.3*1.05, 1.3*1.05^2, 1.3*1.05^3, …, the first payment is Year 5 FCF, which is equal to 1.3*1.05. The value of C/(r-g) with C=1.3*1.05 is the value of the cash flow streams at Year 4.
2.
The free cash flows from year 4 and beyond are 1.3, 1.3*1.05, 1.3*1.05^2, 1.3*1.05^3, …
You can also treat this cash flow streams as a growing perpetuity, C/(r-g), where C=1.3. But note this value of C/(r-g) with C=1.3 is the value of the cash flow streams at Year 3.
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Terminal Value Example
We can restate the free cash flows of the investment as follows (in thousands of dollars):
The total cash flows at Year 4 have two parts:
Year 4 FCF = 1,300.
FCFs from Year 5 to infinity whose value at Year 4 is 27,300.
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| Year | 0 | 1 | 2 | 3 | 4 |
| Free cash Flow (years0−4) | (10,500) | (5,500) | 800 | 1,200 | 1,300 |
| Continuation value (Year 5 and beyond) | Blank | Blank | Blank | Blank | 27,300 |
| Free cash flow | (10,500) | (5,500) | 800 | 1,200 | 28,600 |
Year 4
=$5,597
PV of cash flows in short horizon
PV(FCF at Year 4) + PV(Terminal Value)
Remember to correctly discount terminal value.
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Calculating the NPV
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Present value of the FCF in year t:
NPV of a project:
Sum up PV(FCFt), including PV(FCF0)
e.g. NPV =
See notes underneath the slide
Again, in capital budgeting, a convention is that the project starts at year 0, which is today.
As a result, the initial capital expenditure is in FCF0.
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Considerations in DCF Analysis
Opportunity Costs
Project Externalities
Sunk Costs
Allocated Overhead
Shut Down Costs
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See notes underneath the slide
We will look at these effects because
Some affects incremental revenues and should be included for decision making.
some affects incremental costs and should also be included for decision making.
some should be excluded from decision making.
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Opportunity Costs
The opportunity cost of using a resource is the value it could have provided in its best alternative use.
e.g. suppose a firm bought a production line which will be placed in a warehouse that the company could have otherwise rented out for $20,000 per year.
Should you include this opportunity cost when calculating free cash flow? - see notes below
Calculation: deduct the opportunity cost from the incremental sales.
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See notes underneath the slide
Q: Should you include this opportunity cost when calculating free cash flow?
A: Yes, because the firm forgoes $20,000 when choosing to place the production in the warehouse instead of having it rented out.
The opportunity cost would reduce the firm’s incremental sales annually by the amount of $20,000
The opportunity cost would reduce the firm’s incremental cash flows annually by this amount:
$20,000× (1 − Tax Rate)
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Project Externalities
Indirect effects of the project that may affect the profits of other business activities of the firm.
Cannibalization is when sales of a new product displaces sales of an existing product.
Release of iphone 11 reduces sales of older versions.
Cross-selling is when a new project generates additional demand for existing or other projects.
A new powerful camera may increase sales of existing lenses.
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Sunk Costs
Sunk costs are costs that have been or will be paid regardless of the decision whether or not the investment is undertaken.
Sunk costs should not be included in the incremental earnings analysis.
Past Research and Development Expenditures
Money that has already been spent on R&D is a sunk cost and therefore irrelevant. The decision to continue or abandon a project should be based only on the incremental costs and benefits of the product going forward.
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See notes underneath the slide
For example, suppose after having spent $10,000 on market research, you believe 100% that your new product will generate a NPV of $100.
Note this already spent market research expense is NOT in the calculation of NPV of the project you haven’t undertaken.
Does the market research expense of $10,000 you have already spent affect your decision of the new project?
No. That is a sunk cost.
Should you take the project?
Yes, because the NPV is positive.
What if the NPV of the project is just $1? Again this already spent market research expense is NOT in the calculation of NPV of the project. Should you take the project?
Yes, because the NPV is positive, so PV(benefits) > PV(costs). Note all the costs for this project have been taken out.
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Allocated Overhead
Typically overhead costs are fixed and not incremental to the project and should not be included in the calculation of incremental earnings.
Firms allocate overhead to projects and business units yet, when making decisions about allocating resources to new projects, only new overhead costs that will be actually incurred due to the project should be included.
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Shut Down Costs
There are likely to be costs or benefits occurring incrementally at the end of a project that need to be identified and included.
Costs – employee relocation, severance costs …
Benefits – sale of equipment, intellectual property …
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Reviews of Capital budgeting
Steps:
Estimate incremental cash flows in the project.
Determine a cost of capital used for discounting
Calculate NPV
Accept or reject the project
Key: Recognize all cash flow effects (most challenging)
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Important concepts
capital budgeting
DCF analysis
incremental revenues
change in NWC
unlevered net income
Free Cash Flow (FCF)
marginal tax
depreciation tax shield
accelerated depreciation v.s. straight-line depreciation
terminal value
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Important concepts
Opportunity Costs
Project Externalities (e.g., Cannibalization)
Sunk Costs
Allocated Overhead
Shut Down Costs
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In-class exercise
As the finance manager of a company, you are presented with the following project. The company is considering the purchase of a new piece of equipment which would cost $210,000. This equipment will have a five-year useful life and have a salvage value of $10,000 at the end of the five-year period. It is estimated that
the new equipment will be able to produce 10,000 shelves per year.
the allocated overhead for running the equipment will be $20,000 per year.
they can sell the shelves for $25 each.
the cost of sales is $15 per shelf.
Net Working Capital requirements for the project are as follows:
Year 0 = $10,000
Year 1 = $15,000
Year 2 = $17,000
Year 3 = $15,000
Year 4 = $10,000
The company has a 30% marginal tax rate and a required rate of return of 15%.
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Would you accept this project (support your answer with NPV)?
See notes underneath the slide
Something to think about before you work on it.
What contribute(s) to the free cash flows?
What is the annual depreciation?
What is the net working capital at Year 5? (Hint: when you close a coffee shop, you sell all the beans, collect all the receivable, and of course your suppliers will collect their receivable)
Solution is on Blackboard.
Cash flow from equipment sale
Assuming the equipment will be sold at 10,000 at the end of year 5, the cash inflow = 10,000 (sale price) – 0 (tax) = 10,000. The tax is zero because tax is based on the gain on sale, which by definition is sale price minus book value = 10,000 – 10,000 = 0.
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1
()
(1)(1)
t
tt
tt
tyear discount factor
FCF
PVFCFFCF
rr
=
==´
++
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